cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A116656 Slowest growing sequence of semiprimes having the semiprime-pairwise-sum property: for any i

Original entry on oeis.org

4, 6, 51, 115, 511, 5263, 116623, 204091, 823363, 1144363, 78325123, 883337023, 6860264683, 19613836423, 167589841663
Offset: 1

Views

Author

Zak Seidov, Feb 21 2006

Keywords

Examples

			Triangle of resulting semiprimes begins:
      10
      55,     57
     119,    121,    166
     515,    517,    562,    626
    5267,   5269,   5314,   5378,   5774
  116627, 116629, 116674, 116738, 117134, 121886

Crossrefs

Cf. A001358, A164979, A181620.

Programs

  • Mathematica
    spQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; L = {0, 4}; Do[n = L[[-1]] + 1; While[! AllTrue[n + L, spQ], n++]; AppendTo[L, n], {9}]; Rest@ L (* Giovanni Resta, Jun 13 2018 *)
  • PARI
    lista(nn) = my(m, r, s, t, u, v=vector(nn=max(2, nn))); print1(v[1]=4, ", ", v[2]=6); for(n=3, nn, m=4; r=List([3]); forprime(p=2, oo, if(m*p>v[n-1], break); u=List([]); forprime(q=2, p-1, s=Set(v%(t=p*q)); for(i=1, #s, listput(u, Mod(t-s[i], t)))); s=List([]); for(i=1, #r, forstep(k=r[i], m*p, m, t=1; for(j=1, #u, if(k==u[j], t=0; break)); if(t, listput(s, k)))); r=s; m*=p); listsort(r); forstep(i=0, oo, m, for(j=1, #r, t=i+r[j]; if(t>v[n-1]&&bigomega(t)==2&&bigomega(t+4)==2&&bigomega(t+6)==2, for(k=3, n-1, if(!isprime((t+v[k])\2), t=0; break)); if(t, print1(", ", v[n]=t); break(2)))))); \\ Jinyuan Wang, May 29 2025

Extensions

a(8)-a(10) from R. J. Mathar, Jan 23 2008
a(11)-a(12) from Donovan Johnson, Nov 11 2008
a(13) from Donovan Johnson, Jul 22 2011
a(14) from Giovanni Resta, Jun 13 2018
a(15) from Giovanni Resta, Jun 14 2018

A181622 Sequence starting with 1 such that the sum of any two distinct terms has three distinct prime factors.

Original entry on oeis.org

1, 29, 41, 281, 401, 1089, 1585, 2289, 4629, 27293, 74873, 965813, 2536781, 4479197, 36730306, 150318056, 4527046433
Offset: 1

Views

Author

Michel Lagneau, Jan 31 2011

Keywords

Comments

Choose the first number not leading to a contradiction.

Examples

			Each of the three pairwise sums of the subset {29, 41, 281} is the product of three distinct prime factors: {2*5*7, 2*5*31, 2*7*23}.

Crossrefs

Cf. A180514, A180565, A180615, A181620.

Programs

  • Maple
    with(numtheory):nn:=200000:T:=array(1..nn): U:=array(1..nn): for p from 1 to
  nn do: T[p]:=p:U[p]:=1:od:for u from 1 to 20 do: k:=1+u:for n from u+1 to nn
  do:s:=T[n]+T[u]:s1:=nops(factorset(s)):s2:=bigomega(s):if s1=3 and s2=3 then
  U[k]:=T[n]:k:=k+1:else fi:od:for i from 1 to nn do:T[i]:=U[i]:od:od:for j from
  1 to 30 do:printf(`%d, `, T[j]):od:

Extensions

a(12)-a(17) from Donovan Johnson, Feb 14 2011

A181623 Sequence starting with 1 such that the sum of any two distinct elements has four distinct prime factors.

Original entry on oeis.org

1, 209, 1121, 2989, 11381, 34889, 47701, 62453, 188785, 878185, 1761737, 3931385, 5630905, 7990481, 32892077, 204570037, 253223785, 1353794333, 2877954833
Offset: 1

Views

Author

Michel Lagneau, Jan 31 2011

Keywords

Comments

Choose the first number not leading to a contradiction.

Examples

			Each of the three pairwise sums of the subset {1, 209, 1121} is the product of four distinct prime factors: {2*3*5*7,  2*3*11*17,  2*3*5*137}.

Crossrefs

Cf. A180514, A180565, A180615, A181620, A181622.

Programs

  • Maple
    with(numtheory):nn:=100000:T:=array(1..nn): U:=array(1..nn): for p from 1 to
  nn do: T[p]:=p:U[p]:=1:od:for u from 1 to 30 do: k:=1+u:for n from u+1 to nn
  do:s:=T[n]+T[u]:s1:=nops(factorset(s)):s2:=bigomega(s):if s1=4 and s2=4 then
  U[k]:=T[n]:k:=k+1:else fi:od:for i from 1 to nn do:T[i]:=U[i]:od:od:for j from
  1 to 30 do:printf(`%d, `, T[j]):od:

Extensions

a(9)-a(19) from Donovan Johnson, Feb 14 2011

A305887 The least increasing sequence of numbers where all pairwise sums are semiprimes, with a(1)=4.

Original entry on oeis.org

4, 5, 10, 29, 173, 249, 19073, 71489, 1166789, 3800333, 7021253, 15920129, 84551600693, 224223772673
Offset: 1

Views

Author

Zak Seidov, Jun 14 2018

Keywords

Comments

All terms > 10 are congruent to {3, 9} mod 10.
Triangle of resulting semiprimes begins:
9
14, 15
33, 34, 39
177, 178, 183, 202

Crossrefs

Cf. A001358, A116656, A164979, A181620.

Programs

  • Mathematica
    Nest[Append[#, Block[{k = Last[#] + 1}, While[! AllTrue[#, PrimeOmega[k + #] == 2 &], k++]; k]] &, {4}, 7] (* Michael De Vlieger, Jun 14 2018 *)

Extensions

a(13) from Giovanni Resta, Jun 14 2018
a(14) from Jinyuan Wang, May 29 2025
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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